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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
the differences between the residuals on the GCP and those on 
the Check Point. 
The accuracy of the solution (which can be evaluated in terms 
of residuals on the GCP and on the CHK) varies to a great 
extent with different pseudo-casual initialisation of the network 
weights and different number of neurons, while the initial value 
of the training parameter Jt of the LM algorithm results to be 
quite negligible even though values close to 10? are advisable. 
The architectures of the network that the developed procedure 
is able to verify, depend on some parameters that the operator 
has to supply: 
e the range of variability of the number of neurons: the 
maximum and minimum number of neurons to be tested has 
to be defined. These values are influenced by the number of 
GCPs that are supplied as training pattern. A too high 
number of neurons would decreases the generalisation 
capacity of the network while a too low number would not 
approximate the function in an adequate way. 
e the number of successive initialisations for each node 
architecture: the number of times the training should be 
repeated for each architecture has to be indicated. The 
results that can be obtained, with the same number of 
neurons and same p value can differ greatly according to 
how the weights are initialised. The risk, because of a bad 
initialisation, is that the algorithm stops inside local 
minimums of the performance function. The repetition of 
the training for a sufficiently high number of times (10 
times for this work) prevents from this problem. 
e level of accuracy required of the residuals on the GCPs and 
on the CHKs: the optimal architecture is identified on the 
basis of the simultaneous satisfaction of some conditions: 
[RMSE gp < threshold 
     
  
| RMSE cux € N threshold a) 
where 
r A 7 
RMSE= Du EMS RMS, =JA£ +An, 
N-—1 
The threshold value depends on the expected scale of the 
orthoimage. The simultaneous satisfaction of the two conditions 
helps, in a simple way, to prevent overfitting problems of the 
network (too many neurons) which can be detected, as a first 
approximation, as the difference between RMSEgep and 
RMSEcuk. 
3. RESULTS 
The RFM and MLP non-parametric methods were tested with 
images acquired from different satellite platforms. The accuracy 
of the planimetric positioning was evaluated through the 
evaluation of the residuals on both the GCPs that was used for 
the estimation of the model parameters and on the CHKs 
(which were different from the previous ones). The mean values 
of the residuals were also calculated to show any systematic 
error. A geometrically homogeneous distribution of the GCPs 
on the entire image was maintained during all the tests, as the 
validity of the non-parametric methods decreased with an 
increase in the distance from the support points. 
Tables 3 and 4 report the results that were obtained using the 
polynomial relations and the neural networks. 
  
  
  
  
  
  
  
  
  
  
  
  
N° N? AE An RMSE | RMSE 
Satellite GCPs | CHK | mean | mean | CHK GCP 
S CHK CHK | (pixel) | (pixel) 
Eros Al 51 6 0.00 0.00 3.19 0.83 
QuickBird 60 30 -0.09 0.02 2.76 0.86 
Spots 50 5 -0.02 | -0.09 2.09 1.01 
  
Table 1 — Results obtained through the application of the RFM 
method 
  
N° N° AE AN RMSE | RMSE 
Satellite GCPs | CHKs | Mean | Mean | CHK GCP 
CHK | CHK | (pixel) | (pixel) 
  
  
  
Eros Al 51 6 -0.23 | -1.10 2.46 1.08 
QuickBird 60 30 -0.23 | -0.14 2.37 1.40 
Spots 50 5 -2.04 0.02 2.96 1.38 
  
  
  
  
  
  
  
  
  
Table 2 — Results obtained through the application of the MLP 
neural network method 
4. TRUE ORTHOPHOTO 
The orthoprojection of satellite images is a procedure that is 
used to correctly represent orthogonal projection, on a prefixed 
plane, of the area framed by the sensor during the acquisition. 
This product is obtained through the orthogonal projection of 
each pixel of the image of the territory onto a cartographic 
plane, in such a way that the original perspective representation 
(a deformed cylindrical perspective in the case of pushbroom 
acquisition) is transformed into an equivalent metrically correct 
image. It is in fact possible to measure angles and distances on 
the orthophoto, but also to read the cartographic coordinates of 
significant points exactly like on a map. 
To carry out an orthoprojection it is therefore necessary to have 
a geometric model of the sensor that is able to relate the 3D 
coordinates of the object to the coordinates of the image and a 
digital terrain model (DTM). It is very easy to perform an 
orthoprojection if the surface of the object is continuous (that is, 
smooth), but is not sufficiently accurate if the framed area is an 
urban area and if the geometric resolution of the image is high 
because of numerous discontinuities (breaklines) and frequent 
defilated areas. 
A more complex method should therefore face the following 
problems: 
e the lack of information in correspondence to the defilated 
zones (hidden areas): it is possible to eliminate or limit this 
inconvenience using a multi-image approach, if several 
images of the same area are available (along-track, across- 
track or multitemporal stereoscopy). In the case of a lack of 
images acquired by the same platform, it is possible to use 
the information acquired by other sensors using a multi- 
sensor type approach; 
e the presence of discontinuities: this problem is resolved 
using more rigorous interpolation methods for the 
generation of a DTM whose grids are made up of a large 
number of points (DTM dense or Dense DTM). A dense 
DTM therefore allows a correct description of a surface to 
be obtained, a description that also takes into account the 
height of the buildings.